Abstract
The Moran sets and the Moran class are defined by geometric fashion that distinguishes the classical self-similar sets from the following points:
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(i)
The placements of the basic sets at each step of the constructions can be arbitrary.
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(ii)
The contraction ratios may be different at each step.
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(iii)
The lower limit of the contraction ratios permits zero.
The properties of the Moran sets and Moran class are studied, and the Hausdorff, packing and upper Box-counting dimensions of the Moran sets are determined by net measure techniques. It is shown that some important properties of the self-similar sets no longer hold for Moran sets.
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Hua, S., Rao, H., Wen, Z. et al. On the Structures and dimensions of Moran sets. Sci. China Ser. A-Math. 43, 836–852 (2000). https://doi.org/10.1007/BF02884183
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DOI: https://doi.org/10.1007/BF02884183